Even answers

p. 66

52. (b)

54. (a)

72. True since the limit can be split into the lim 1 and lim sin(x)/x as x approaches 0.

p. 84

14. Everywhere in [–1, 3) except for x = 0, 1, 2.

54. False. Consider f(x) = 1/x which is continuous and has a point of discontinuity at x = 0.

p. 124

32. 1/sqrt(x) + 1/(2xsqrt(x))
54. True. Since f'(x) = –1/x^2 is never zero, there are no horizontal tangents.

p. 126

1. D
2. A
4.
a. x = 0 and ±sqrt(2)
b. y = –4x + 1
c. y = 1/4x – 13/4

Unit 2 IW #2

solutions

Unit 2 IW #4

solutions

p. 124

14. (x^2 – 3)/x^2 which is the same as 1 – 3/x^2
56. D
58. B

Unit 2 Quiz 1

solutions

p. 135

40. False- it's the absolute value of velocity.
42. C

p. 146

26.
a. Prove using the quotient rule on cos(x)/sin(x). Don't forget that great Pythagorean Identity...
b. Prove using the quotient rule on 1/sin(x).

p. 148

2. A
4.
a. 2 m
b. Typo!!! Should say "Find the *instantaneous* velocity..." or just "Find the velocity..." So, v(t) = –2t + 1 m/sec
c. 0 ≤ t ≤ 0.5
d. a(t) = –2 m/s^2
e. 3 m/sec

p. 158

58. a. 1 b. 6 c. 1 d. –1/9 e. –40/3 f. –6 g. –4/9
72. E

p. 167

62. A
64. C

Unit 2 IW #8

solutions

p. 169

2. B
4.
a.
b. y + 2 = 2(x – 1) and y = 3
c. fifth root of –24

p. 171/Exploration 1

1. Yes!
2. f'(x) = 5x4 +2 Since this function is always positive, f is always increasing- hence, it passes the horizontal line test and is one-to-one (i.e. has an inverse).
3. Do it!
4. Do it!
5. (1, 2)
6. 7
7. 1/7
8. 1/7

Unit 2 IW #10 & 11

solutions

p. 198

46. False- consider a 5th degree polynomial with four relative extrema...
48. E
50. B
52. a. No b. No c. No d. min value is 0 at x = –3, 0, and 3 and local max at (–sqrt(3), 6sqrt(3)) and
(sqrt(3), 6sqrt(3)).

p. 206

54. B
56. D

Unit 3 IW #2

solutions

p. 219

56. True- this is the Second Derivative Test for a local maximum.
58. E
60. A

p. 231

20. 4/sqrt(21) (which is about 0.87 miles) down the shore from the point nearest her boat
22. radius = 10sqrt(2/3) (about 8.16 cm)
height = 20/(sqrt(3)) (about 11.55 cm)
volume = 4000π/(3sqrt(3)) (about 2418.40 cm3)
56. E

Section 5-4

solutions

p. 248

60. D
62. A

Section 5-6

solutions

Unit 4 IW #1

solutions

Unit 4 IW #2

solutions

Unit 4 IW #4

solutions

Unit 4 IW #5

solutions

Unit 4 IW #6

solutions

Unit 4 IW #8

solutions
p. 294
46. False- consider an odd function from -a to a. The area below the x-axis cancels the area above the x-axis.
48. D
50. C

Unit 4 IW #9

p. 297
2. B
4.
a. f(x) = x3 + 6x2 + 4x – 5
b. –3

Unit 4 IW #10

solutions

Unit 4 IW #11

p. 320
54.
a. 0
b. –1
c. –π

p. 377
40. (d)
42. (a)

Unit 5 IW #1

p. 342
32. -2/3(cot(x))^(3/2) + C
34. 1/4(tan(x/2))^8 + C
48. tan(x) + (tan(x))^3/3 + C
54. 1/3
76. A

Unit 5 IW #2

p. 390
32. True. Since the velocity is positive, the integral of the velocity is equal to the integral of its absolute value, which is the total distance traveled.
34. D
36. A

Unit 5 IW #3

p. 399
2. 4π/3
4. 4/3
10. 5/6
14. 49/6
52. A
54. B

Unit 5 IW #4

p. 410
66. E

Unit 5 Quiz 1

solutions

Unit 5 IW #5

solutions
p. 411
68. D

Unit 5 IW #6 & #7

FRQ scoring guidelines